doi: 10.5028/jatm.2012.04044412 Multidisciplinary Design Optimization of Sounding Rocket Fins Shape Using a Tool Called MDO-SONDA Alexandre Nogueira Barbosa1*, Lamartine Nogueira Frutuoso Guimarães2 1,QVWLWXWRGH$HURQiXWLFDH(VSDoR±6mR-RVpGRV&DPSRV63±%UD]LO 2,QVWLWXWRGH(VWXGRV$YDQoDGRV±6mR-RVpGRV&DPSRV63±%UD]LO Abstract:0XOWLGLVFLSOLQDU\GHVLJQRSWLPL]DWLRQLVDSURPLVLQJ¿HOGLQDHURVSDFHHQJLQHHULQJ+RZHYHUDGYDQFHVLQWKLV ¿HOGKDYHQRWEHHQDSSOLHG\HWWRLPSURYH%UD]LOLDQVRXQGLQJURFNHWVVXFKDVWKH967KHUHIRUHWRJLYHDSHUVSHF WLYHRIWKHPXOWLGLVFLSOLQDU\GHVLJQRSWLPL]DWLRQLQWKLVFRQWH[WWKLVZRUNSUHVHQWHGDFDVHVWXG\RIWKLVURFNHWZKLFK FRQVLVWVRIWKHVKDSHRSWLPL]DWLRQRILWV¿QV7RDFKLHYHWKLVJRDODVSHFLDOWRROFDOOHG0'2621'$ZKLFKLVWKHPDLQ FRQWULEXWLRQRIWKLVZRUNZDVGHYHORSHG,WVFXUUHQWYHUVLRQLQWHUDFWVZLWKWZRKLJK¿GHOLW\H[HFXWDEOHFRGHVRQHRI DHURG\QDPLFVDQGDQRWKHURIWUDMHFWRU\H[SORLWLQJWKHV\QHUJ\EHWZHHQERWKGLVFLSOLQHV7KH0'2621'$LVEDVHGRQ DPXOWLREMHFWLYHJHQHWLFDOJRULWKPZKRVHUHDORSHUDWRUZDVRULJLQDOO\GHVLJQHGLQWKLVZRUN%\XVLQJWKHSURSRVHGWRRO LWZDVIRXQGWKDWWKHGUDJGXHWRWKHURFNHW¿QVFRXOGEHUHGXFHGXSWRZLWKRXWLQFUHDVLQJWKHFKDQFHVRIDGYHUVH HIIHFWVWKDWFRXOGOHDGWRXQVWDEOHEHKDYLRUV Keywords:6RXQGLQJURFNHW5RFNHW¿QGHVLJQ0XOWLGLVFLSOLQDU\GHVLJQRSWLPL]DWLRQ0XOWLREMHFWLYHJHQHWLFDOJRULWKPV INTRODUCTION At the end of the 1990s, among the Brazilian sounding respect to the entire project, promoted by low synergy between rockets, the VS-40 was presented as one that provides the best the design disciplines. conditions for experiments in microgravity (Ribeiro, 1999). 6LQFHZKHQWKH¿UVW96ZDVODXQFKHGWKH Space systems are complex, i.e., their behavior is governed methodology that allows exploiting the synergy between by many distinct but interacting physical phenomena, and its design disciplines has not been used yet for Brazilian multidisciplinary, requiring balance among competing sounding rockets. A methodology called multidisciplinary objectives related to safety, reliability, performance, design optimization (MDO) replaces the traditional operability, and cost (Rowell and Korte, 2003). Over time, sequential methodology by synergic interactions between the advances in the engineering of complex systems have allowed design disciplines, promoting the overall gain in products to more quickly identify feasible solutions and exploit the performance, decreasing the design time (Floudas and synergy among the design disciplines (Rowell and Korte, Pardalos, 2009). +RZHYHUWKH96KDVQRWEHHQEHQH¿WHGE\VXFK Why should the VS-40 be revised? It promises the best advances yet. The interactions between the design disciplines conditions for microgravity experiments, but not widely of the VS-40 were processed in a sequential order, in which launched yet such as the VSB-30, also a Brazilian sounding those disciplines that act early in the conceptual design rocket, so that it could be more studied, and perhaps improved establish constraints on the others that follow later, leading E\FRQVLGHULQJFROOHFWHGÀLJKWGDWD7KH96ZDVUHFHQWO\ to a concept without regarding the trade-offs that may exist PRGL¿HGDWWKH*HUPDQ$HURVSDFH&HQWHU '/5 LQRUGHUWR between the design objectives. The plausible consequence SURYLGHWKHUHTXLUHGVWDELOLW\IRUDVSHFL¿FPLVVLRQEHFDXVH of such sequential methodology is a suboptimal design with it was not originally designed for carrying a payload with exposed canards, indicating that its design can be altered, if Received: 31/07/12 Accepted: 08/10/12 QHFHVVDU\WREHQH¿WLWVVWDELOLW\DQGSHUKDSVLWVSHUIRUPDQFH *author for correspondence: [email protected] /DVWO\LWKDVQRWEHHQEHQH¿WHGE\DGYDQFHVLQWKHHQJLQHHULQJ 3UDoD0DUHFKDO(GXDUGR*RPHV±9LODGDV$FiFLDV of complex systems, and it may have some subsystems that &(36mR-RVpGRV&DPSRV63±%UD]LO could be improved regarding its next launches at Brazilian J. Aerosp. Technol. Manag., São José dos Campos, Vol.4, No 4, pp. 431-442, Oct.-Dec., 2012 431 %DUERVD$1*XLPDUmHV/1) territory carrying the Sub-orbital SARA, a Brazilian platform for microgravity experiments with an advantage, the payload for microgravity experiments. recovery operation associated with the VSB-30 is less costly Motivated by a search for VS-40 improvements, the use WKDQZLWKWKH96ZKRVHVSODVKGRZQLVDSSUR[LPDWHO\¿YH of the MDO was introduced in Brazilian sounding rockets. times more distant from the continent-ocean boundary than the Therefore, the objective of this paper was to provide a VSB-30, demanding more autonomy for the recovery means. perspective of the MDO application in this context based on a From 2004 to 2010, ten VSB-30 campaigns were case study of the VS-40. As case study, the shape optimization successfully performed, three of them in the Brazilian territory RI WKH 96 ¿QV ZDV SURSRVHG LQ RUGHU WR LPSURYH LWV *DUFLDHWDO, 2011). In contrast to the VSB-30, three VS-40 SHUIRUPDQFHE\UHGXFLQJWKHGUDJGXHWRWKH¿QVZLWKRXW campaigns has occurred so far, two of them in the Brazilian increasing the chances of adverse effects that could lead to WHUULWRU\WKH¿UVWRQHLQ6DQWD0DULDFDPSDLJQ )LJD unstable behaviors. To perform the optimization, a computer DQGWKHVHFRQGRQHLQ/LYUDPHQWRFDPSDLJQ )LJE tool called MDO-SONDA (MDO of Sounding Rockets), ERWKDWWKH$OFkQWDUD/DXQFK&HQWHU &/$ LQ0DUDQKmR ,$( which was developed by Alexandre Nogueira Barbosa, was 2Q-XQHDPRGL¿HG96FDOOHG960 XVHG0'2621'$SUHVHQWDWLRQLQWKHOLWHUDWXUHZDV¿UVW carrying the Sharp Edge Flight Experiment (SHEFEX) II introduced by this paper. (Weihs HWDOD D*HUPDQSURMHFWZDVVXFFHVVIXOO\ launched at the Andøya Rocket Range in Northern Norway SOUNDING ROCKETS AND MICROGRAVITY '/5 DQGLW EHFDPHWKH¿UVW96 RSHUDWLRQLQ ENVIRONMENT DQRWKHUFRXQWU\ )LJF 7KH960¿QVVKDSH )LJF LV VLJQL¿FDQWO\ GLIIHUHQW IURP WKH WZR SUHYLRXV 96 Sounding rockets, such as the VS-40, are characterized by )LJVDDQGE 7KHQHZ¿QVZHUHGHVLJQHGDQGFRQVWUXFWHG WKHLUDSSOLFDWLRQDQGÀLJKWSUR¿OH$FFRUGLQJWR0RQWHQEUXFN IRU6+()(;,,DW'/5GXHWRWKHQHHGRIH[WHQGHG¿QVWR HWDO (2001), such rockets are constituted of solid fueled motors compensate for the aerodynamic effects of the small canards and a payload that carries instruments to take measurements at the payload, as can be seen in Fig. 1c (Weihs HWDO, 2008). DQGSHUIRUPVFLHQWL¿FH[SHULPHQWVGXULQJDSDUDEROLFÀLJKW In 1997, a recovery orbital platform called SARA Thus, the sounding term means taking measurements. for supporting short-orbital experiments in microgravity In comparison with the VSB-30, the VS-40 bi-stage can environment was proposed (Moraes and Pilchowski, 1997). provide a wide exposure to the microgravity environment, ,Q FRPSDULVRQ ZLWK D VXERUELWDO ÀLJKW ZKLFK SURYLGHV D characterized by a condition where an object is subjected few minutes of microgravity conditions, an orbital one can WRDJIRUFHOHVVWKDQȝJ /D1HYHDQG&RUUrD-U provide more than ten days before reentering the Earths achieved by moving in free fall, where there are no forces DWPRVSKHUH7KH6SDFH&DSVXOH5HFRYHU\([SHULPHQW 65( other than gravity acting on the object. ZKLFKLVDQ,QGLDQVSDFHFUDIW¿UVWODXQFKHGLQLVDYHU\ Payloads carried by rockets achieve the microgravity environment after the burnout of the rocket when the thrust force is zero and the payload is above the atmosphere. It is assumed that the Kármán line, at 100 km above the seawater surface, might be used as a reference for microgravity H[SHULPHQW SXUSRVHV WR GH¿QH WKH ERXQGDU\ EHWZHHQ WKH atmosphere and the outer space, from which the atmosphere becomes so thin that the drag force could be neglected. FACTS ABOUT THE VS-40 In spite of the fact that the VS-40 provides more exposure to microgravity than the VSB-30, since the 21st century began, (a) (b) (c) rather than the VS-40, the VSB-30 has been most frequently Sources: (a) and (b) Institute of Aeronautics and Space, Brazil; XVHG IRU PLFURJUDYLW\ H[SHULPHQWV *DUFLD HW DO, 2011). F '/5 &HUWDLQO\EHFDXVHWKH96%KDVPHWPLVVLRQUHTXLUHPHQWV Figure 1. VS-40 launches. 432 J. Aerosp. Technol. Manag., São José dos Campos, Vol.4, No 4, pp. 431-442, Oct.-Dec., 2012 0XOWLGLVFLSOLQDU\'HVLJQ2SWLPL]DWLRQRI6RXQGLQJ5RFNHW)LQV6KDSH8VLQJD7RRO&DOOHG0'2621'$ similar example of such a kind of platform (Reddy, 2007). The current version is only prepared for optimization of $OVRDQH[DPSOHLVWKH5(;)UHH)O\HUWKH*HUPDQSURSRVDO WKHVKDSHRIURFNHW¿QV+RZHYHULWLVDQREMHFWRULHQWHGFRGH for application of SHEFEX derived technology, which ZULWWHQLQ&WKDWSURYLGHVVSHFL¿FIRUPVFODVVHVDQGREMHFWV is a reusable orbital return vehicle for experiments under to structure proper interfaces for further studies, including microgravity conditions (Weihs HWDO, 2008b). the shape optimization of other rocket subsystems, such as Thereafter, a platform called Sub-orbital SARA, which is DGGLWLRQDOVHWRI¿QVQRVHIDLULQJSURWXEHUDQFHVDQGFRQLFDO part of the road map to achieve the orbital mission purpose transitions between rocket stages of different diameters. of this platform, has been constructed to be launched by a The main aspects of the MDO-SONDA are architecture, VS-40, supporting an experimental module to be exposed to inputs, outputs, optimization algorithm, and how to proceed PLFURJUDYLW\HQYLURQPHQW /D1HYHDQG&RUUrD with the optimization. 7KH96ZDVRULJLQDOO\GHVLJQHGIRUÀLJKWTXDOL¿FDWLRQ of the S44 motor, which constitutes the fourth stage of the Architecture %UD]LOLDQODXQFKYHKLFOH 9/6 3HUHLUDDQG0RUDHV-U ,QZKHQWKH¿UVW96ZDVODXQFKHGWKH0'2 The architecture of the MDO-SONDA is described in methodology had recently been presented. two parts: the interaction between the objective function and 7KHVKDSHRSWLPL]DWLRQRIWKH96¿QVZLOOEHSUHVHQWHGWZRKLJK¿GHOLW\H[HFXWDEOHFRGHVRQHRIDHURG\QDPLFVDQG as a case study using such methodology to demonstrate its another of trajectory